Influence of model validation on proper selection of process models—an industrial case study

Application of Gaussian processes for black-box modelling of biosystems

“…Their overview can be found e.g. in [12,22]. The most important are model plausibility, model falseness and model purposiveness, explained as follows.…”

“…For the validation and comparison of different identified models the same performance measures were used as in illustrative example, i.e. negative log-likelihood of identification data (14), mean relative square error (12), log-predictive density (13) and visual inspection of the validation data. Values of the performance measures for only some among many of the identified GP models can be seen in Table 2 to illustrate the main search direction among the different sets of regressors.…”

“…The lack of the identification data in this study is even more stressed than in the previous example. Several combinations of regressors for the first order model structures were tried and the models were validated with the visual inspection and the use of performance measures MRSE (12) and LD (13) of the one-step ahead prediction results on validation data. Due to the scarce information contained in the identification data there was no significant difference between identified models, making regressor selection hard to pursue.…”

“…First, to present the procedure of dynamic system identification using the model based on Gaussian processes. Second, within this framework emphasis is placed on validation, which includes several features [12]: the model purposiveness, the model plausibility and model falseness. Within these two objectives, the use of properties differentiating the GP model from other approaches, i.e prediction variance and the way the input/output relations are encompassed, is emphasised.…”

Modeling of the denitrification/anaerobic digestion process of salmon fishery wastewater in a biofilm tubular reactor

“…The Theil inequality coefficient, TIC (Theil, 1970) was used as the model validation criterion as suggested by Hvala et al (2005). When compared to the simple sum of the squared errors, the principal advantage of the Theil inequality coefficient is that it varies between 0 and 1.…”